%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : SEU679^2 : TPTP v9.2.1. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n012.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jun 3 08:52:42 AM UTC 2026 % Result : Theorem 0.15s 0.38s % Output : Proof 0.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.06 % Problem : SEU679^2 : TPTP v9.2.1. Released v3.7.0. % 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.07/0.25 % Computer : n012.cluster.edu % 0.07/0.25 % Model : x86_64 x86_64 % 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.25 % Memory : 8042.1875MB % 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.25 % CPULimit : 300 % 0.07/0.25 % WCLimit : 300 % 0.07/0.25 % DateTime : Tue Jun 2 17:45:48 EDT 2026 % 0.07/0.25 % CPUTime : % 0.15/0.33 %----Proving TH0 % 0.15/0.38 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 0.15/0.38 % SZS status Theorem % 0.15/0.38 % SZS output start Proof % 0.15/0.38 ( % 0.15/0.38 (declare-sort $$unsorted 0) % 0.15/0.38 (declare-const tptp.emptyset $$unsorted) % 0.15/0.38 (declare-const tptp.setadjoin (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.38 (declare-const tptp.in (-> $$unsorted $$unsorted Bool)) % 0.15/0.38 (declare-const tptp.dsetconstr (-> $$unsorted (-> $$unsorted Bool) $$unsorted)) % 0.15/0.38 (declare-const tptp.cartprod (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.38 (declare-const tptp.subset (-> $$unsorted $$unsorted Bool)) % 0.15/0.38 (declare-const tptp.kpair (-> $$unsorted $$unsorted $$unsorted)) % 0.15/0.38 (declare-const tptp.dpsetconstr (-> $$unsorted $$unsorted (-> $$unsorted $$unsorted Bool) $$unsorted)) % 0.15/0.38 (declare-const tptp.lamProp Bool) % 0.15/0.38 (define tptp.singleton () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (lambda (@list _let_2) (exists (@list _let_1) (and (_ (_ tptp.in _let_1) _let_2) (= _let_2 (_ (_ tptp.setadjoin _let_1) tptp.emptyset)))))))) % 0.15/0.38 (define tptp.ex1 () (let ((_let_1 (@var "Xx" $$unsorted))) (let ((_let_2 (@var "Xphi" (-> $$unsorted Bool)))) (let ((_let_3 (@var "A" $$unsorted))) (lambda (@list _let_3 _let_2) (_ tptp.singleton (_ (_ tptp.dsetconstr _let_3) (lambda (@list _let_1) (_ _let_2 _let_1))))))))) % 0.15/0.38 (define tptp.breln () (let ((_let_1 (@var "B" $$unsorted))) (let ((_let_2 (@var "A" $$unsorted))) (let ((_let_3 (@var "C" $$unsorted))) (lambda (@list _let_2 _let_1 _let_3) (_ (_ tptp.subset _let_3) (_ (_ tptp.cartprod _let_2) _let_1))))))) % 0.15/0.38 (define tptp.func () (let ((_let_1 (@var "R" $$unsorted))) (let ((_let_2 (@var "Xy" $$unsorted))) (let ((_let_3 (@var "Xx" $$unsorted))) (let ((_let_4 (@var "B" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_4 _let_1) (and (_ (_ (_ tptp.breln _let_5) _let_4) _let_1) (forall (@list _let_3) (=> (_ (_ tptp.in _let_3) _let_5) (_ (_ tptp.ex1 _let_4) (lambda (@list _let_2) (_ (_ tptp.in (_ (_ tptp.kpair _let_3) _let_2)) _let_1))))))))))))) % 0.15/0.38 (define tptp.lam () (let ((_let_1 (@var "Xy" $$unsorted))) (let ((_let_2 (@var "Xx" $$unsorted))) (let ((_let_3 (@var "Xf" (-> $$unsorted $$unsorted)))) (let ((_let_4 (@var "B" $$unsorted))) (let ((_let_5 (@var "A" $$unsorted))) (lambda (@list _let_5 _let_4 _let_3) (_ (_ (_ tptp.dpsetconstr _let_5) _let_4) (lambda (@list _let_2 _let_1) (= (_ _let_3 _let_2) _let_1)))))))))) % 0.15/0.38 (define @t1 () (@var "Xy" $$unsorted)) % 0.15/0.38 (define @t2 () (@var "Xx" $$unsorted)) % 0.15/0.38 (define @t3 () (@var "Xf" (-> $$unsorted $$unsorted))) % 0.15/0.38 (define @t4 () (_ @t3 @t2)) % 0.15/0.38 (define @t5 () (@list @t2 @t1)) % 0.15/0.38 (define @t6 () (lambda @t5 (= @t4 @t1))) % 0.15/0.38 (define @t7 () (@var "B" $$unsorted)) % 0.15/0.38 (define @t8 () (@var "A" $$unsorted)) % 0.15/0.38 (define @t9 () (_ (_ tptp.dpsetconstr @t8) @t7)) % 0.15/0.38 (define @t10 () (_ @t9 @t6)) % 0.15/0.38 (define @t11 () (_ (_ tptp.func @t8) @t7)) % 0.15/0.38 (define @t12 () (_ (_ tptp.in @t4) @t7)) % 0.15/0.38 (define @t13 () (_ (_ tptp.in @t2) @t8)) % 0.15/0.38 (define @t14 () (@list @t2)) % 0.15/0.38 (define @t15 () (forall @t14 (=> @t13 @t12))) % 0.15/0.38 (define @t16 () (=> @t15 (_ @t11 @t10))) % 0.15/0.38 (define @t17 () (@list @t8 @t7 @t3)) % 0.15/0.38 (define @t18 () (forall @t17 @t16)) % 0.15/0.38 (define @t19 () (= tptp.lamProp @t18)) % 0.15/0.38 (define @t20 () (lambda @t14 @t4)) % 0.15/0.38 (define @t21 () (=> @t15 (_ @t11 (_ (_ (_ tptp.lam @t8) @t7) @t20)))) % 0.15/0.38 (define @t22 () (forall @t17 @t21)) % 0.15/0.38 (define @t23 () (=> tptp.lamProp @t22)) % 0.15/0.38 (define @t24 () (not @t23)) % 0.15/0.38 (define @t25 () (_ (_ tptp.setadjoin @t2) tptp.emptyset)) % 0.15/0.38 (define @t26 () (= @t8 @t25)) % 0.15/0.38 (define @t27 () (and @t13 @t26)) % 0.15/0.38 (define @t28 () (exists @t14 @t27)) % 0.15/0.38 (define @t29 () (@list @t8)) % 0.15/0.38 (define @t30 () (lambda @t29 @t28)) % 0.15/0.38 (define @t31 () (@var "Xphi" (-> $$unsorted Bool))) % 0.15/0.38 (define @t32 () (lambda @t14 (_ @t31 @t2))) % 0.15/0.38 (define @t33 () (_ tptp.dsetconstr @t8)) % 0.15/0.38 (define @t34 () (_ @t33 @t32)) % 0.15/0.38 (define @t35 () (@list @t8 @t31)) % 0.15/0.38 (define @t36 () (lambda @t35 (_ tptp.singleton @t34))) % 0.15/0.38 (define @t37 () (_ (_ tptp.cartprod @t8) @t7)) % 0.15/0.38 (define @t38 () (@var "C" $$unsorted)) % 0.15/0.38 (define @t39 () (_ (_ tptp.subset @t38) @t37)) % 0.15/0.38 (define @t40 () (lambda (@list @t8 @t7 @t38) @t39)) % 0.15/0.38 (define @t41 () (@var "R" $$unsorted)) % 0.15/0.38 (define @t42 () (_ (_ tptp.kpair @t2) @t1)) % 0.15/0.38 (define @t43 () (_ (_ tptp.in @t42) @t41)) % 0.15/0.38 (define @t44 () (@list @t1)) % 0.15/0.38 (define @t45 () (lambda @t44 @t43)) % 0.15/0.38 (define @t46 () (=> @t13 (_ (_ tptp.ex1 @t7) @t45))) % 0.15/0.38 (define @t47 () (forall @t14 @t46)) % 0.15/0.38 (define @t48 () (and (_ (_ (_ tptp.breln @t8) @t7) @t41) @t47)) % 0.15/0.38 (define @t49 () (@list @t8 @t7 @t41)) % 0.15/0.38 (define @t50 () (lambda @t49 @t48)) % 0.15/0.38 (define @t51 () (lambda @t17 @t10)) % 0.15/0.38 (define @t52 () (@var "BOUND_VARIABLE_7775" $$unsorted)) % 0.15/0.38 (define @t53 () (_ @t3 @t52)) % 0.15/0.38 (define @t54 () (@var "BOUND_VARIABLE_7736" $$unsorted)) % 0.15/0.38 (define @t55 () (@list @t52 @t54)) % 0.15/0.38 (define @t56 () (tptp.dpsetconstr @t8 @t7 (lambda @t55 (= @t54 @t53)))) % 0.15/0.38 (define @t57 () (@var "BOUND_VARIABLE_7828" $$unsorted)) % 0.15/0.38 (define @t58 () (tptp.dsetconstr @t7 (lambda @t44 (tptp.in (tptp.kpair @t57 @t1) @t56)))) % 0.15/0.38 (define @t59 () (@var "BOUND_VARIABLE_7579" $$unsorted)) % 0.15/0.38 (define @t60 () (tptp.setadjoin @t59 tptp.emptyset)) % 0.15/0.38 (define @t61 () (@list @t59)) % 0.15/0.38 (define @t62 () (or (not (tptp.in @t57 @t8)) (not (forall @t61 (or (not (tptp.in @t59 @t58)) (not (= @t60 @t58))))))) % 0.15/0.38 (define @t63 () (tptp.cartprod @t8 @t7)) % 0.15/0.38 (define @t64 () (_ @t3 @t2)) % 0.15/0.38 (define @t65 () (= @t1 @t64)) % 0.15/0.38 (define @t66 () (lambda @t5 @t65)) % 0.15/0.38 (define @t67 () (tptp.dpsetconstr @t8 @t7 @t66)) % 0.15/0.38 (define @t68 () (tptp.subset @t67 @t63)) % 0.15/0.38 (define @t69 () (and @t68 @t62)) % 0.15/0.38 (define @t70 () (tptp.in @t64 @t7)) % 0.15/0.38 (define @t71 () (tptp.in @t2 @t8)) % 0.15/0.38 (define @t72 () (not @t71)) % 0.15/0.38 (define @t73 () (forall @t14 (or @t72 @t70))) % 0.15/0.38 (define @t74 () (not @t73)) % 0.15/0.38 (define @t75 () (or @t74 @t69)) % 0.15/0.38 (define @t76 () (forall (@list @t8 @t7 @t3 @t57) @t75)) % 0.15/0.38 (define @t77 () (@list @t57)) % 0.15/0.38 (define @t78 () (forall @t77 @t75)) % 0.15/0.38 (define @t79 () (forall @t77 @t62)) % 0.15/0.38 (define @t80 () (@list @t2)) % 0.15/0.38 (define @t81 () (forall @t77 @t68)) % 0.15/0.38 (define @t82 () (and @t81 @t79)) % 0.15/0.38 (define @t83 () (forall @t77 @t69)) % 0.15/0.38 (define @t84 () (or @t74 @t83)) % 0.15/0.38 (define @t85 () (tptp.kpair @t2 @t1)) % 0.15/0.38 (define @t86 () (tptp.dsetconstr @t7 (lambda @t44 (tptp.in @t85 @t56)))) % 0.15/0.38 (define @t87 () (forall @t14 (or @t72 (not (forall @t61 (or (not (tptp.in @t59 @t86)) (not (= @t60 @t86)))))))) % 0.15/0.38 (define @t88 () (= @t1 @t4)) % 0.15/0.38 (define @t89 () (lambda @t5 @t88)) % 0.15/0.38 (define @t90 () (_ @t9 @t89)) % 0.15/0.38 (define @t91 () (_ (_ tptp.subset @t90) @t37)) % 0.15/0.38 (define @t92 () (and @t91 @t87)) % 0.15/0.38 (define @t93 () (or @t74 @t92)) % 0.15/0.38 (define @t94 () (lambda @t55 (= @t53 @t54))) % 0.15/0.38 (define @t95 () (tptp.dpsetconstr @t8 @t7 @t94)) % 0.15/0.38 (define @t96 () (tptp.in @t85 @t95)) % 0.15/0.38 (define @t97 () (lambda @t44 @t96)) % 0.15/0.38 (define @t98 () (tptp.dsetconstr @t7 @t97)) % 0.15/0.38 (define @t99 () (= @t60 @t98)) % 0.15/0.38 (define @t100 () (not @t99)) % 0.15/0.38 (define @t101 () (tptp.in @t59 @t98)) % 0.15/0.38 (define @t102 () (not @t101)) % 0.15/0.38 (define @t103 () (or @t102 @t100)) % 0.15/0.38 (define @t104 () (forall @t61 @t103)) % 0.15/0.38 (define @t105 () (not @t104)) % 0.15/0.38 (define @t106 () (or @t72 @t105)) % 0.15/0.38 (define @t107 () (= @t64 @t54)) % 0.15/0.38 (define @t108 () (@list @t2 @t54)) % 0.15/0.38 (define @t109 () (lambda @t108 @t107)) % 0.15/0.38 (define @t110 () (tptp.dpsetconstr @t8 @t7 @t109)) % 0.15/0.38 (define @t111 () (tptp.in @t85 @t110)) % 0.15/0.38 (define @t112 () (lambda @t44 @t111)) % 0.15/0.38 (define @t113 () (tptp.dsetconstr @t7 @t112)) % 0.15/0.38 (define @t114 () (= @t60 @t113)) % 0.15/0.38 (define @t115 () (not @t114)) % 0.15/0.38 (define @t116 () (tptp.in @t59 @t113)) % 0.15/0.38 (define @t117 () (not @t116)) % 0.15/0.38 (define @t118 () (or @t117 @t115)) % 0.15/0.38 (define @t119 () (forall @t61 @t118)) % 0.15/0.38 (define @t120 () (not @t119)) % 0.15/0.38 (define @t121 () (or @t72 @t120)) % 0.15/0.38 (define @t122 () (= @t4 @t54)) % 0.15/0.38 (define @t123 () (lambda @t108 @t122)) % 0.15/0.38 (define @t124 () (_ @t9 @t123)) % 0.15/0.38 (define @t125 () (tptp.in @t85 @t124)) % 0.15/0.38 (define @t126 () (lambda @t44 @t125)) % 0.15/0.38 (define @t127 () (tptp.dsetconstr @t7 @t126)) % 0.15/0.38 (define @t128 () (= @t60 @t127)) % 0.15/0.38 (define @t129 () (not @t128)) % 0.15/0.38 (define @t130 () (tptp.in @t59 @t127)) % 0.15/0.38 (define @t131 () (not @t130)) % 0.15/0.38 (define @t132 () (or @t131 @t129)) % 0.15/0.38 (define @t133 () (lambda @t108 (= @t54 @t4))) % 0.15/0.38 (define @t134 () (tptp.in @t85 (_ @t9 @t133))) % 0.15/0.38 (define @t135 () (lambda @t44 @t134)) % 0.15/0.38 (define @t136 () (lambda @t44 (tptp.in @t85 @t90))) % 0.15/0.38 (define @t137 () (tptp.dsetconstr @t7 @t136)) % 0.15/0.38 (define @t138 () (= @t60 @t137)) % 0.15/0.38 (define @t139 () (not @t138)) % 0.15/0.38 (define @t140 () (tptp.in @t59 @t137)) % 0.15/0.38 (define @t141 () (not @t140)) % 0.15/0.38 (define @t142 () (or @t141 @t139)) % 0.15/0.38 (define @t143 () (forall @t61 @t142)) % 0.15/0.38 (define @t144 () (not @t143)) % 0.15/0.38 (define @t145 () (or @t72 @t144)) % 0.15/0.38 (define @t146 () (forall @t14 @t145)) % 0.15/0.38 (define @t147 () (and @t91 @t146)) % 0.15/0.38 (define @t148 () (tptp.in @t85 @t41)) % 0.15/0.38 (define @t149 () (tptp.dsetconstr @t7 (lambda @t44 @t148))) % 0.15/0.38 (define @t150 () (not (forall @t61 (or (not (tptp.in @t59 @t149)) (not (= @t60 @t149)))))) % 0.15/0.38 (define @t151 () (_ (_ tptp.subset @t41) @t37)) % 0.15/0.38 (define @t152 () (and @t151 (forall @t14 (or @t72 @t150)))) % 0.15/0.38 (define @t153 () (lambda (@list @t41) @t152)) % 0.15/0.38 (define @t154 () (_ @t20 @t2)) % 0.15/0.38 (define @t155 () (= @t1 @t154)) % 0.15/0.38 (define @t156 () (lambda @t5 @t155)) % 0.15/0.38 (define @t157 () (lambda (@list @t3) @t90)) % 0.15/0.38 (define @t158 () (lambda (@list @t7 @t3) @t90)) % 0.15/0.38 (define @t159 () (_ (lambda @t17 @t90) @t8)) % 0.15/0.38 (define @t160 () (lambda (@list @t7 @t41) @t152)) % 0.15/0.38 (define @t161 () (_ (lambda @t49 @t152) @t8)) % 0.15/0.38 (define @t162 () (not @t13)) % 0.15/0.38 (define @t163 () (or @t162 @t12)) % 0.15/0.38 (define @t164 () (_ @t161 @t7)) % 0.15/0.38 (define @t165 () (=> @t15 (_ @t164 (_ (_ @t159 @t7) @t20)))) % 0.15/0.38 (define @t166 () (forall @t17 @t165)) % 0.15/0.38 (define @t167 () (=> tptp.lamProp @t166)) % 0.15/0.38 (define @t168 () (or @t162 @t150)) % 0.15/0.38 (define @t169 () (tptp.dsetconstr @t7 @t45)) % 0.15/0.38 (define @t170 () (= @t60 @t169)) % 0.15/0.38 (define @t171 () (not @t170)) % 0.15/0.38 (define @t172 () (tptp.in @t59 @t169)) % 0.15/0.38 (define @t173 () (not @t172)) % 0.15/0.38 (define @t174 () (or @t173 @t171)) % 0.15/0.38 (define @t175 () (not (= @t169 @t60))) % 0.15/0.38 (define @t176 () (or @t173 @t175)) % 0.15/0.38 (define @t177 () (forall @t61 @t176)) % 0.15/0.38 (define @t178 () (not @t177)) % 0.15/0.38 (define @t179 () (tptp.dsetconstr @t7 @t31)) % 0.15/0.38 (define @t180 () (not (tptp.in @t59 @t179))) % 0.15/0.38 (define @t181 () (@list @t31)) % 0.15/0.38 (define @t182 () (not (= @t60 @t179))) % 0.15/0.38 (define @t183 () (or @t180 @t182)) % 0.15/0.38 (define @t184 () (forall @t61 @t183)) % 0.15/0.38 (define @t185 () (not @t184)) % 0.15/0.38 (define @t186 () (tptp.setadjoin @t2 tptp.emptyset)) % 0.15/0.38 (define @t187 () (forall @t14 (or (not (tptp.in @t2 @t179)) (not (= @t186 @t179))))) % 0.15/0.38 (define @t188 () (not @t187)) % 0.15/0.38 (define @t189 () (lambda @t181 @t188)) % 0.15/0.38 (define @t190 () (tptp.dsetconstr @t8 @t31)) % 0.15/0.38 (define @t191 () (_ (lambda @t35 (not (forall @t14 (or (not (tptp.in @t2 @t190)) (not (= @t186 @t190)))))) @t7)) % 0.15/0.38 (define @t192 () (=> @t13 (_ @t191 @t45))) % 0.15/0.38 (define @t193 () (forall @t14 @t192)) % 0.15/0.38 (define @t194 () (lambda (@list @t38) @t39)) % 0.15/0.38 (define @t195 () (lambda (@list @t7 @t38) @t39)) % 0.15/0.38 (define @t196 () (_ @t40 @t8)) % 0.15/0.38 (define @t197 () (@var "BOUND_VARIABLE_7478" $$unsorted)) % 0.15/0.38 (define @t198 () (_ @t31 @t197)) % 0.15/0.38 (define @t199 () (@list @t197)) % 0.15/0.38 (define @t200 () (lambda @t199 @t198)) % 0.15/0.38 (define @t201 () (tptp.dsetconstr @t8 @t200)) % 0.15/0.38 (define @t202 () (= @t186 @t201)) % 0.15/0.38 (define @t203 () (not @t202)) % 0.15/0.38 (define @t204 () (tptp.in @t2 @t201)) % 0.15/0.38 (define @t205 () (not @t204)) % 0.15/0.38 (define @t206 () (or @t205 @t203)) % 0.15/0.38 (define @t207 () (_ @t31 @t197)) % 0.15/0.38 (define @t208 () (lambda @t199 @t207)) % 0.15/0.38 (define @t209 () (_ @t33 @t208)) % 0.15/0.38 (define @t210 () (= @t186 @t209)) % 0.15/0.38 (define @t211 () (not @t210)) % 0.15/0.38 (define @t212 () (tptp.in @t2 @t209)) % 0.15/0.38 (define @t213 () (not @t212)) % 0.15/0.38 (define @t214 () (or @t213 @t211)) % 0.15/0.38 (define @t215 () (= @t186 @t34)) % 0.15/0.38 (define @t216 () (not @t215)) % 0.15/0.38 (define @t217 () (tptp.in @t2 @t34)) % 0.15/0.38 (define @t218 () (not @t217)) % 0.15/0.38 (define @t219 () (or @t218 @t216)) % 0.15/0.38 (define @t220 () (not (= @t34 @t186))) % 0.15/0.38 (define @t221 () (or @t218 @t220)) % 0.15/0.38 (define @t222 () (forall @t14 @t221)) % 0.15/0.38 (define @t223 () (not @t222)) % 0.15/0.38 (define @t224 () (not @t26)) % 0.15/0.38 (define @t225 () (or @t162 @t224)) % 0.15/0.38 (define @t226 () (forall @t14 (not @t27))) % 0.15/0.38 (define @t227 () (not @t226)) % 0.15/0.38 (define @t228 () (=> @t15 (_ @t164 @t10))) % 0.15/0.38 (define @t229 () (forall @t17 @t228)) % 0.15/0.38 (assume @p1 @t19) % 0.15/0.38 (assume @p2 @t24) % 0.15/0.38 (assume @p3 true) % 0.15/0.38 (step @p4 (= tptp.singleton @t30) :rule refl :args (@t30)) % 0.15/0.38 (step @p5 (= tptp.ex1 @t36) :rule refl :args (@t36)) % 0.15/0.38 (step @p6 (= tptp.breln @t40) :rule refl :args (@t40)) % 0.15/0.38 (step @p7 (= tptp.func @t50) :rule refl :args (@t50)) % 0.15/0.38 (step @p8 (= tptp.lam @t51) :rule refl :args (@t51)) % 0.15/0.38 (step @p9 :rule quant-merge-prenex :args ((= (forall @t17 @t78) @t76))) % 0.15/0.38 (step @p10 :rule alpha_equiv :args (@t79 (@list @t57) @t80)) % 0.15/0.38 (step @p11 :rule quant-unused-vars :args ((= @t81 @t68))) % 0.15/0.38 (step @p12 :rule nary_cong :premises (@p11 @p10) :args (@t82)) % 0.15/0.38 (step @p13 :rule quant-miniscope-and :args ((= @t83 @t82))) % 0.15/0.38 (step @p14 :rule trans :premises (@p13 @p12)) % 0.15/0.38 (step @p15 :rule refl :args (@t74)) % 0.15/0.38 (step @p16 :rule nary_cong :premises (@p15 @p14) :args (@t84)) % 0.15/0.38 (step @p17 :rule quant-miniscope-or :args ((= @t78 @t84))) % 0.15/0.38 (step @p18 :rule trans :premises (@p17 @p16)) % 0.15/0.38 (step @p19 :rule symm :premises (@p18)) % 0.15/0.38 (step @p20 :rule cong :premises (@p19) :args ((forall @t17 (or @t74 (and @t68 @t87))))) % 0.15/0.38 (step @p21 :rule trans :premises (@p20 @p9)) % 0.15/0.38 (step @p22 :rule refl :args (@t87)) % 0.15/0.38 (step @p23 :rule refl :args ((tptp.subset @t90 @t37))) % 0.15/0.38 (step @p24 :rule refl :args (@t63)) % 0.15/0.38 (step @p25 :rule refl :args ((tptp.dpsetconstr @t8 @t7 @t89))) % 0.15/0.38 (step @p26 :rule refl :args (@t64)) % 0.15/0.38 (step @p27 :rule refl :args (@t1)) % 0.15/0.38 (step @p28 :rule cong :premises (@p27 @p26) :args (@t65)) % 0.15/0.38 (step @p29 :rule cong :premises (@p28) :args (@t66)) % 0.15/0.38 (step @p30 :rule refl :args (@t7)) % 0.15/0.38 (step @p31 :rule refl :args (@t8)) % 0.15/0.38 (step @p32 :rule cong :premises (@p31 @p30 @p29) :args (@t67)) % 0.15/0.38 (step @p33 :rule trans :premises (@p32 @p25)) % 0.15/0.38 (step @p34 :rule cong :premises (@p33 @p24) :args (@t68)) % 0.15/0.38 (step @p35 :rule trans :premises (@p34 @p23)) % 0.15/0.38 (step @p36 :rule refl :args (tptp.subset)) % 0.15/0.38 (step @p37 :rule ho_cong :premises (@p36 @p33)) % 0.15/0.38 (step @p38 :rule ho_cong :premises (@p37 @p24)) % 0.15/0.38 (step @p39 :rule cong :premises (@p38 @p35) :args ((= (_ (_ tptp.subset @t67) @t63) @t68))) % 0.15/0.38 (step @p40 :rule symm :premises (@p39)) % 0.15/0.38 (step @p41 :rule refl :args (@t91)) % 0.15/0.38 (step @p42 :rule eq_resolve :premises (@p41 @p40)) % 0.15/0.38 (step @p43 :rule refl :args (@t37)) % 0.15/0.38 (step @p44 :rule cong :premises (@p43 @p24) :args ((= @t37 @t63))) % 0.15/0.38 (step @p45 :rule symm :premises (@p44)) % 0.15/0.38 (step @p46 :rule eq_resolve :premises (@p43 @p45)) % 0.15/0.38 (step @p47 :rule refl :args (@t9)) % 0.15/0.38 (step @p48 :rule ho_cong :premises (@p47 @p29)) % 0.15/0.38 (step @p49 :rule cong :premises (@p48 @p33) :args ((= (_ @t9 @t66) @t67))) % 0.15/0.38 (step @p50 :rule symm :premises (@p49)) % 0.15/0.38 (step @p51 :rule refl :args (@t90)) % 0.15/0.38 (step @p52 :rule eq_resolve :premises (@p51 @p50)) % 0.15/0.38 (step @p53 :rule refl :args (@t4)) % 0.15/0.38 (step @p54 :rule cong :premises (@p53 @p26) :args ((= @t4 @t64))) % 0.15/0.38 (step @p55 :rule symm :premises (@p54)) % 0.15/0.38 (step @p56 :rule eq_resolve :premises (@p53 @p55)) % 0.15/0.38 (step @p57 :rule cong :premises (@p27 @p56) :args (@t88)) % 0.15/0.38 (step @p58 :rule cong :premises (@p57) :args (@t89)) % 0.15/0.38 (step @p59 :rule ho_cong :premises (@p47 @p58)) % 0.15/0.38 (step @p60 :rule trans :premises (@p59 @p52)) % 0.15/0.38 (step @p61 :rule ho_cong :premises (@p36 @p60)) % 0.15/0.38 (step @p62 :rule ho_cong :premises (@p61 @p46)) % 0.15/0.38 (step @p63 :rule trans :premises (@p62 @p42)) % 0.15/0.38 (step @p64 :rule nary_cong :premises (@p63 @p22) :args (@t92)) % 0.15/0.38 (step @p65 :rule nary_cong :premises (@p15 @p64) :args (@t93)) % 0.15/0.38 (step @p66 :rule cong :premises (@p65) :args ((forall @t17 @t93))) % 0.15/0.38 (step @p67 :rule trans :premises (@p66 @p21)) % 0.15/0.38 (step @p68 :rule bool-impl-elim :args (@t73 @t92)) % 0.15/0.38 (step @p69 :rule cong :premises (@p68) :args ((forall @t17 (=> @t73 @t92)))) % 0.15/0.38 (step @p70 :rule trans :premises (@p69 @p67)) % 0.15/0.38 (step @p71 :rule eq-symm :args (@t53 @t54)) % 0.15/0.38 (step @p72 :rule cong :premises (@p71) :args (@t94)) % 0.15/0.38 (step @p73 :rule refl :args (@t7)) % 0.15/0.38 (step @p74 :rule refl :args (@t8)) % 0.15/0.38 (step @p75 :rule cong :premises (@p74 @p73 @p72) :args (@t95)) % 0.15/0.38 (step @p76 :rule refl :args (@t85)) % 0.15/0.38 (step @p77 :rule cong :premises (@p76 @p75) :args (@t96)) % 0.15/0.38 (step @p78 :rule cong :premises (@p77) :args (@t97)) % 0.15/0.38 (step @p79 :rule cong :premises (@p73 @p78) :args (@t98)) % 0.15/0.38 (step @p80 :rule refl :args (@t60)) % 0.15/0.38 (step @p81 :rule cong :premises (@p80 @p79) :args (@t99)) % 0.15/0.38 (step @p82 :rule cong :premises (@p81) :args (@t100)) % 0.15/0.38 (step @p83 :rule refl :args (@t59)) % 0.15/0.38 (step @p84 :rule cong :premises (@p83 @p79) :args (@t101)) % 0.15/0.38 (step @p85 :rule cong :premises (@p84) :args (@t102)) % 0.15/0.38 (step @p86 :rule nary_cong :premises (@p85 @p82) :args (@t103)) % 0.15/0.38 (step @p87 :rule cong :premises (@p86) :args (@t104)) % 0.15/0.38 (step @p88 :rule cong :premises (@p87) :args (@t105)) % 0.15/0.38 (step @p89 :rule refl :args (@t72)) % 0.15/0.38 (step @p90 :rule nary_cong :premises (@p89 @p88) :args (@t106)) % 0.15/0.38 (step @p91 :rule cong :premises (@p90) :args ((forall @t14 @t106))) % 0.15/0.38 (step @p92 :rule alpha_equiv :args (@t109 @t80 (@list @t52))) % 0.15/0.38 (step @p93 :rule cong :premises (@p31 @p30 @p92) :args (@t110)) % 0.15/0.38 (step @p94 :rule refl :args (@t85)) % 0.15/0.38 (step @p95 :rule cong :premises (@p94 @p93) :args (@t111)) % 0.15/0.38 (step @p96 :rule cong :premises (@p95) :args (@t112)) % 0.15/0.38 (step @p97 :rule cong :premises (@p30 @p96) :args (@t113)) % 0.15/0.38 (step @p98 :rule refl :args (@t60)) % 0.15/0.38 (step @p99 :rule cong :premises (@p98 @p97) :args (@t114)) % 0.15/0.38 (step @p100 :rule cong :premises (@p99) :args (@t115)) % 0.15/0.38 (step @p101 :rule refl :args (@t59)) % 0.15/0.38 (step @p102 :rule cong :premises (@p101 @p97) :args (@t116)) % 0.15/0.38 (step @p103 :rule cong :premises (@p102) :args (@t117)) % 0.15/0.38 (step @p104 :rule nary_cong :premises (@p103 @p100) :args (@t118)) % 0.15/0.38 (step @p105 :rule cong :premises (@p104) :args (@t119)) % 0.15/0.38 (step @p106 :rule cong :premises (@p105) :args (@t120)) % 0.15/0.38 (step @p107 :rule refl :args (@t72)) % 0.15/0.38 (step @p108 :rule nary_cong :premises (@p107 @p106) :args (@t121)) % 0.15/0.38 (step @p109 :rule cong :premises (@p108) :args ((forall @t14 @t121))) % 0.15/0.38 (step @p110 :rule trans :premises (@p109 @p91)) % 0.15/0.38 (step @p111 :rule refl :args ((tptp.dpsetconstr @t8 @t7 @t123))) % 0.15/0.38 (step @p112 :rule refl :args (@t54)) % 0.15/0.38 (step @p113 :rule cong :premises (@p26 @p112) :args (@t107)) % 0.15/0.38 (step @p114 :rule cong :premises (@p113) :args (@t109)) % 0.15/0.38 (step @p115 :rule cong :premises (@p31 @p30 @p114) :args (@t110)) % 0.15/0.38 (step @p116 :rule trans :premises (@p115 @p111)) % 0.15/0.38 (step @p117 :rule ho_cong :premises (@p47 @p114)) % 0.15/0.38 (step @p118 :rule cong :premises (@p117 @p116) :args ((= (_ @t9 @t109) @t110))) % 0.15/0.38 (step @p119 :rule symm :premises (@p118)) % 0.15/0.38 (step @p120 :rule refl :args (@t124)) % 0.15/0.38 (step @p121 :rule eq_resolve :premises (@p120 @p119)) % 0.15/0.38 (step @p122 :rule cong :premises (@p56 @p112) :args (@t122)) % 0.15/0.38 (step @p123 :rule cong :premises (@p122) :args (@t123)) % 0.15/0.38 (step @p124 :rule ho_cong :premises (@p47 @p123)) % 0.15/0.38 (step @p125 :rule trans :premises (@p124 @p121)) % 0.15/0.38 (step @p126 :rule cong :premises (@p94 @p125) :args (@t125)) % 0.15/0.38 (step @p127 :rule cong :premises (@p126) :args (@t126)) % 0.15/0.38 (step @p128 :rule cong :premises (@p30 @p127) :args (@t127)) % 0.15/0.38 (step @p129 :rule cong :premises (@p98 @p128) :args (@t128)) % 0.15/0.38 (step @p130 :rule cong :premises (@p129) :args (@t129)) % 0.15/0.38 (step @p131 :rule cong :premises (@p101 @p128) :args (@t130)) % 0.15/0.38 (step @p132 :rule cong :premises (@p131) :args (@t131)) % 0.15/0.38 (step @p133 :rule nary_cong :premises (@p132 @p130) :args (@t132)) % 0.15/0.38 (step @p134 :rule cong :premises (@p133) :args ((forall @t61 @t132))) % 0.15/0.38 (step @p135 :rule eq-symm :args (@t54 @t4)) % 0.15/0.38 (step @p136 :rule cong :premises (@p135) :args (@t133)) % 0.15/0.38 (step @p137 :rule refl :args (@t9)) % 0.15/0.38 (step @p138 :rule ho_cong :premises (@p137 @p136)) % 0.15/0.38 (step @p139 :rule cong :premises (@p76 @p138) :args (@t134)) % 0.15/0.38 (step @p140 :rule cong :premises (@p139) :args (@t135)) % 0.15/0.38 ; WARNING: add trust step for TRUST_THEORY_REWRITE % 0.15/0.38 ; trust TRUST_THEORY_REWRITE % 0.15/0.38 (step @p141 :rule trust :premises () :args ((= @t136 @t135))) % 0.15/0.38 (step @p142 :rule trans :premises (@p141 @p140)) % 0.15/0.38 (step @p143 :rule cong :premises (@p73 @p142) :args (@t137)) % 0.15/0.38 (step @p144 :rule cong :premises (@p80 @p143) :args (@t138)) % 0.15/0.38 (step @p145 :rule cong :premises (@p144) :args (@t139)) % 0.15/0.38 (step @p146 :rule cong :premises (@p83 @p143) :args (@t140)) % 0.15/0.38 (step @p147 :rule cong :premises (@p146) :args (@t141)) % 0.15/0.38 (step @p148 :rule nary_cong :premises (@p147 @p145) :args (@t142)) % 0.15/0.38 (step @p149 :rule cong :premises (@p148) :args (@t143)) % 0.15/0.38 (step @p150 :rule trans :premises (@p149 @p134)) % 0.15/0.38 (step @p151 :rule cong :premises (@p150) :args (@t144)) % 0.15/0.38 (step @p152 :rule nary_cong :premises (@p89 @p151) :args (@t145)) % 0.15/0.38 (step @p153 :rule cong :premises (@p152) :args (@t146)) % 0.15/0.38 (step @p154 :rule trans :premises (@p153 @p110)) % 0.15/0.38 (step @p155 :rule refl :args (@t91)) % 0.15/0.38 (step @p156 :rule nary_cong :premises (@p155 @p154) :args (@t147)) % 0.15/0.38 (step @p157 :rule beta-reduce :args ((= (_ @t153 @t90) @t147))) % 0.15/0.38 (step @p158 :rule trans :premises (@p157 @p156)) % 0.15/0.38 (step @p159 :rule beta-reduce :args ((= @t154 @t4))) % 0.15/0.38 (step @p160 :rule refl :args (@t1)) % 0.15/0.38 (step @p161 :rule cong :premises (@p160 @p159) :args (@t155)) % 0.15/0.38 (step @p162 :rule cong :premises (@p161) :args (@t156)) % 0.15/0.38 (step @p163 :rule ho_cong :premises (@p137 @p162)) % 0.15/0.38 (step @p164 :rule beta-reduce :args ((= (_ @t157 @t20) (_ @t9 @t156)))) % 0.15/0.38 (step @p165 :rule trans :premises (@p164 @p163)) % 0.15/0.38 (step @p166 :rule refl :args (@t20)) % 0.15/0.38 (step @p167 :rule beta-reduce :args ((= (_ @t158 @t7) @t157))) % 0.15/0.38 (step @p168 :rule beta-reduce :args ((= @t159 @t158))) % 0.15/0.38 (step @p169 :rule ho_cong :premises (@p168 @p73)) % 0.15/0.38 (step @p170 :rule trans :premises (@p169 @p167)) % 0.15/0.38 (step @p171 :rule ho_cong :premises (@p170 @p166)) % 0.15/0.38 (step @p172 :rule trans :premises (@p171 @p165)) % 0.15/0.38 (step @p173 :rule beta-reduce :args ((= (_ @t160 @t7) @t153))) % 0.15/0.38 (step @p174 :rule beta-reduce :args ((= @t161 @t160))) % 0.15/0.38 (step @p175 :rule ho_cong :premises (@p174 @p73)) % 0.15/0.38 (step @p176 :rule trans :premises (@p175 @p173)) % 0.15/0.38 (step @p177 :rule ho_cong :premises (@p176 @p172)) % 0.15/0.38 (step @p178 :rule trans :premises (@p177 @p158)) % 0.15/0.38 (step @p179 :rule refl :args ((tptp.in @t4 @t7))) % 0.15/0.38 (step @p180 :rule cong :premises (@p26 @p30) :args (@t70)) % 0.15/0.38 (step @p181 :rule trans :premises (@p180 @p179)) % 0.15/0.38 (step @p182 :rule refl :args (tptp.in)) % 0.15/0.38 (step @p183 :rule ho_cong :premises (@p182 @p26)) % 0.15/0.38 (step @p184 :rule ho_cong :premises (@p183 @p30)) % 0.15/0.38 (step @p185 :rule cong :premises (@p184 @p181) :args ((= (_ (_ tptp.in @t64) @t7) @t70))) % 0.15/0.38 (step @p186 :rule symm :premises (@p185)) % 0.15/0.38 (step @p187 :rule refl :args (@t12)) % 0.15/0.38 (step @p188 :rule eq_resolve :premises (@p187 @p186)) % 0.15/0.38 (step @p189 :rule ho_cong :premises (@p182 @p56)) % 0.15/0.38 (step @p190 :rule ho_cong :premises (@p189 @p30)) % 0.15/0.38 (step @p191 :rule trans :premises (@p190 @p188)) % 0.15/0.38 (step @p192 :rule refl :args (@t71)) % 0.15/0.38 (step @p193 :rule refl :args (@t13)) % 0.15/0.38 (step @p194 :rule cong :premises (@p193 @p192) :args ((= @t13 @t71))) % 0.15/0.38 (step @p195 :rule symm :premises (@p194)) % 0.15/0.38 (step @p196 :rule eq_resolve :premises (@p193 @p195)) % 0.15/0.38 (step @p197 :rule 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@p212 :rule cong :premises (@p211) :args (@t51)) % 0.15/0.38 (step @p213 :rule trans :premises (@p8 @p212)) % 0.15/0.38 (step @p214 :rule ho_cong :premises (@p213 @p74)) % 0.15/0.38 (step @p215 :rule ho_cong :premises (@p214 @p73)) % 0.15/0.38 (step @p216 :rule ho_cong :premises (@p215 @p166)) % 0.15/0.38 (step @p217 :rule refl :args (@t150)) % 0.15/0.38 (step @p218 :rule nary_cong :premises (@p197 @p217) :args (@t168)) % 0.15/0.38 (step @p219 :rule cong :premises (@p218) :args ((forall @t14 @t168))) % 0.15/0.38 (step @p220 :rule bool-impl-elim :args (@t13 @t150)) % 0.15/0.38 (step @p221 :rule cong :premises (@p220) :args ((forall @t14 (=> @t13 @t150)))) % 0.15/0.38 (step @p222 :rule trans :premises (@p221 @p219)) % 0.15/0.38 (step @p223 :rule refl :args ((tptp.in @t42 @t41))) % 0.15/0.38 (step @p224 :rule refl :args (@t41)) % 0.15/0.38 (step @p225 :rule refl :args (@t85)) % 0.15/0.38 (step @p226 :rule cong :premises (@p225 @p224) :args (@t148)) % 0.15/0.38 (step @p227 :rule trans :premises (@p226 @p223)) % 0.15/0.38 (step @p228 :rule ho_cong :premises (@p182 @p225)) % 0.15/0.38 (step @p229 :rule ho_cong :premises (@p228 @p224)) % 0.15/0.38 (step @p230 :rule cong :premises (@p229 @p227) :args ((= (_ (_ tptp.in @t85) @t41) @t148))) % 0.15/0.38 (step @p231 :rule symm :premises (@p230)) % 0.15/0.38 (step @p232 :rule refl :args (@t43)) % 0.15/0.38 (step @p233 :rule eq_resolve :premises (@p232 @p231)) % 0.15/0.38 (step @p234 :rule refl :args (@t42)) % 0.15/0.38 (step @p235 :rule cong :premises (@p234 @p225) :args ((= @t42 @t85))) % 0.15/0.38 (step @p236 :rule symm :premises (@p235)) % 0.15/0.38 (step @p237 :rule eq_resolve :premises (@p234 @p236)) % 0.15/0.38 (step @p238 :rule ho_cong :premises (@p182 @p237)) % 0.15/0.38 (step @p239 :rule ho_cong :premises (@p238 @p224)) % 0.15/0.38 (step @p240 :rule trans :premises (@p239 @p233)) % 0.15/0.38 (step @p241 :rule cong :premises (@p240) :args (@t45)) % 0.15/0.38 (step @p242 :rule cong :premises (@p30 @p241) :args (@t169)) % 0.15/0.38 (step @p243 :rule cong :premises (@p98 @p242) :args (@t170)) % 0.15/0.38 (step @p244 :rule cong :premises (@p243) :args (@t171)) % 0.15/0.38 (step @p245 :rule cong :premises (@p101 @p242) :args (@t172)) % 0.15/0.38 (step @p246 :rule cong :premises (@p245) :args (@t173)) % 0.15/0.38 (step @p247 :rule nary_cong :premises (@p246 @p244) :args (@t174)) % 0.15/0.38 (step @p248 :rule cong :premises (@p247) :args ((forall @t61 @t174))) % 0.15/0.38 (step @p249 :rule eq-symm :args (@t169 @t60)) % 0.15/0.38 (step @p250 :rule cong :premises (@p249) :args (@t175)) % 0.15/0.38 (step @p251 :rule refl :args (@t173)) % 0.15/0.38 (step @p252 :rule nary_cong :premises (@p251 @p250) :args (@t176)) % 0.15/0.38 (step @p253 :rule cong :premises (@p252) :args (@t177)) % 0.15/0.38 (step @p254 :rule trans :premises (@p253 @p248)) % 0.15/0.38 (step @p255 :rule cong :premises (@p254) :args (@t178)) % 0.15/0.38 (step @p256 :rule beta-reduce :args ((= (_ (lambda @t181 (not (forall @t61 (or @t180 (not (= @t179 @t60)))))) @t45) @t178))) % 0.15/0.38 (step @p257 :rule trans :premises (@p256 @p255)) % 0.15/0.38 (step @p258 :rule refl :args (@t45)) % 0.15/0.38 (step @p259 :rule eq-symm :args (@t60 @t179)) % 0.15/0.38 (step @p260 :rule cong :premises (@p259) :args (@t182)) % 0.15/0.38 (step @p261 :rule refl :args (@t180)) % 0.15/0.38 (step @p262 :rule nary_cong :premises (@p261 @p260) :args (@t183)) % 0.15/0.38 (step @p263 :rule cong :premises (@p262) :args (@t184)) % 0.15/0.38 (step @p264 :rule cong :premises (@p263) :args (@t185)) % 0.15/0.38 (step @p265 :rule cong :premises (@p264) :args ((lambda @t181 @t185))) % 0.15/0.38 (step @p266 :rule ho_cong :premises (@p265 @p258)) % 0.15/0.38 (step @p267 :rule trans :premises (@p266 @p257)) % 0.15/0.38 (step @p268 :rule refl :args (@t45)) % 0.15/0.38 (step @p269 :rule alpha_equiv :args (@t187 @t80 (@list @t59))) % 0.15/0.38 (step @p270 :rule cong :premises (@p269) :args (@t188)) % 0.15/0.38 (step @p271 :rule cong :premises (@p270) :args (@t189)) % 0.15/0.38 (step @p272 :rule ho_cong :premises (@p271 @p268)) % 0.15/0.38 (step @p273 :rule trans :premises (@p272 @p267)) % 0.15/0.38 (step @p274 :rule beta-reduce :args ((= @t191 @t189))) % 0.15/0.38 (step @p275 :rule ho_cong :premises (@p274 @p258)) % 0.15/0.38 (step @p276 :rule trans :premises (@p275 @p273)) % 0.15/0.38 (step @p277 :rule refl :args (@t13)) % 0.15/0.38 (step @p278 :rule cong :premises (@p277 @p276) :args (@t192)) % 0.15/0.38 (step @p279 :rule cong :premises (@p278) :args (@t193)) % 0.15/0.38 (step @p280 :rule trans :premises (@p279 @p222)) % 0.15/0.38 (step @p281 :rule beta-reduce :args ((= (_ @t194 @t41) @t151))) % 0.15/0.38 (step @p282 :rule refl :args (@t41)) % 0.15/0.38 (step @p283 :rule beta-reduce :args ((= (_ @t195 @t7) @t194))) % 0.15/0.38 (step @p284 :rule beta-reduce :args ((= @t196 @t195))) % 0.15/0.38 (step @p285 :rule ho_cong :premises (@p284 @p73)) % 0.15/0.38 (step @p286 :rule trans :premises (@p285 @p283)) % 0.15/0.38 (step @p287 :rule ho_cong :premises (@p286 @p282)) % 0.15/0.38 (step @p288 :rule trans :premises (@p287 @p281)) % 0.15/0.38 (step @p289 :rule nary_cong :premises (@p288 @p280) :args ((and (_ (_ @t196 @t7) @t41) @t193))) % 0.15/0.38 (step @p290 :rule lambda-elim :args ((= @t200 @t31))) % 0.15/0.38 (step @p291 :rule cong :premises (@p74 @p290) :args (@t201)) % 0.15/0.38 (step @p292 :rule refl :args (@t186)) % 0.15/0.38 (step @p293 :rule cong :premises (@p292 @p291) :args (@t202)) % 0.15/0.38 (step @p294 :rule cong :premises (@p293) :args (@t203)) % 0.15/0.38 (step @p295 :rule refl :args (@t2)) % 0.15/0.38 (step @p296 :rule cong :premises (@p295 @p291) :args (@t204)) % 0.15/0.38 (step @p297 :rule cong :premises (@p296) :args (@t205)) % 0.15/0.38 (step @p298 :rule nary_cong :premises (@p297 @p294) :args (@t206)) % 0.15/0.38 (step @p299 :rule cong :premises (@p298) :args ((forall @t14 @t206))) % 0.15/0.38 (step @p300 :rule refl :args ((tptp.dsetconstr @t8 @t208))) % 0.15/0.38 (step @p301 :rule refl :args (@t198)) % 0.15/0.38 (step @p302 :rule cong :premises (@p301) :args (@t200)) % 0.15/0.38 (step @p303 :rule cong :premises (@p31 @p302) :args (@t201)) % 0.15/0.38 (step @p304 :rule trans :premises (@p303 @p300)) % 0.15/0.38 (step @p305 :rule refl :args (@t33)) % 0.15/0.38 (step @p306 :rule ho_cong :premises (@p305 @p302)) % 0.15/0.38 (step @p307 :rule cong :premises (@p306 @p304) :args ((= (_ @t33 @t200) @t201))) % 0.15/0.38 (step @p308 :rule symm :premises (@p307)) % 0.15/0.38 (step @p309 :rule refl :args (@t209)) % 0.15/0.38 (step @p310 :rule eq_resolve :premises (@p309 @p308)) % 0.15/0.38 (step @p311 :rule refl :args (@t207)) % 0.15/0.38 (step @p312 :rule cong :premises (@p311 @p301) :args ((= @t207 @t198))) % 0.15/0.38 (step @p313 :rule symm :premises (@p312)) % 0.15/0.38 (step @p314 :rule eq_resolve :premises (@p311 @p313)) % 0.15/0.38 (step @p315 :rule cong :premises (@p314) :args (@t208)) % 0.15/0.38 (step @p316 :rule ho_cong :premises (@p305 @p315)) % 0.15/0.38 (step @p317 :rule trans :premises (@p316 @p310)) % 0.15/0.38 (step @p318 :rule refl :args (@t186)) % 0.15/0.38 (step @p319 :rule cong :premises (@p318 @p317) :args (@t210)) % 0.15/0.38 (step @p320 :rule cong :premises (@p319) :args (@t211)) % 0.15/0.38 (step @p321 :rule refl :args (@t2)) % 0.15/0.38 (step @p322 :rule cong :premises (@p321 @p317) :args (@t212)) % 0.15/0.38 (step @p323 :rule cong :premises (@p322) :args (@t213)) % 0.15/0.38 (step @p324 :rule nary_cong :premises (@p323 @p320) :args (@t214)) % 0.15/0.38 (step @p325 :rule cong :premises (@p324) :args ((forall @t14 @t214))) % 0.15/0.38 (step @p326 :rule trans :premises (@p325 @p299)) % 0.15/0.38 (step @p327 :rule alpha_equiv :args (@t32 @t80 (@list @t197))) % 0.15/0.38 (step @p328 :rule ho_cong :premises (@p305 @p327)) % 0.15/0.38 (step @p329 :rule cong :premises (@p318 @p328) :args (@t215)) % 0.15/0.38 (step @p330 :rule cong :premises (@p329) :args (@t216)) % 0.15/0.38 (step @p331 :rule cong :premises (@p321 @p328) :args (@t217)) % 0.15/0.38 (step @p332 :rule cong :premises (@p331) :args (@t218)) % 0.15/0.38 (step @p333 :rule nary_cong :premises (@p332 @p330) :args (@t219)) % 0.15/0.38 (step @p334 :rule cong :premises (@p333) :args ((forall @t14 @t219))) % 0.15/0.38 (step @p335 :rule trans :premises (@p334 @p326)) % 0.15/0.38 (step @p336 :rule eq-symm :args (@t34 @t186)) % 0.15/0.38 (step @p337 :rule cong :premises (@p336) :args (@t220)) % 0.15/0.38 (step @p338 :rule refl :args (@t218)) % 0.15/0.38 (step @p339 :rule nary_cong :premises (@p338 @p337) :args (@t221)) % 0.15/0.38 (step @p340 :rule cong :premises (@p339) :args (@t222)) % 0.15/0.38 (step @p341 :rule trans :premises (@p340 @p335)) % 0.15/0.38 (step @p342 :rule cong :premises (@p341) :args (@t223)) % 0.15/0.38 (step @p343 :rule beta-reduce :args ((= (_ (lambda @t29 (not (forall @t14 (or @t72 (not (= @t8 @t186)))))) @t34) @t223))) % 0.15/0.38 (step @p344 :rule trans :premises (@p343 @p342)) % 0.15/0.38 (step @p345 :rule refl :args (@t34)) % 0.15/0.38 (step @p346 :rule refl :args (@t186)) % 0.15/0.38 (step @p347 :rule refl :args (@t25)) % 0.15/0.38 (step @p348 :rule cong :premises (@p347 @p346) :args ((= @t25 @t186))) % 0.15/0.38 (step @p349 :rule symm :premises (@p348)) % 0.15/0.38 (step @p350 :rule eq_resolve :premises (@p347 @p349)) % 0.15/0.38 (step @p351 :rule cong :premises (@p31 @p350) :args (@t26)) % 0.15/0.38 (step @p352 :rule cong :premises (@p351) :args (@t224)) % 0.15/0.38 (step @p353 :rule nary_cong :premises (@p197 @p352) :args (@t225)) % 0.15/0.38 (step @p354 :rule cong :premises (@p353) :args ((forall @t14 @t225))) % 0.15/0.38 (step @p355 :rule bool-and-de-morgan :args (@t13 @t26 true)) % 0.15/0.38 (step @p356 :rule cong :premises (@p355) :args (@t226)) % 0.15/0.38 (step @p357 :rule trans :premises (@p356 @p354)) % 0.15/0.38 (step @p358 :rule cong :premises (@p357) :args (@t227)) % 0.15/0.38 (step @p359 :rule exists-elim :args ((= @t28 @t227))) % 0.15/0.38 (step @p360 :rule trans :premises (@p359 @p358)) % 0.15/0.38 (step @p361 :rule cong :premises (@p360) :args (@t30)) % 0.15/0.38 (step @p362 :rule trans :premises (@p4 @p361)) % 0.15/0.38 (step @p363 :rule ho_cong :premises (@p362 @p345)) % 0.15/0.38 (step @p364 :rule trans :premises (@p363 @p344)) % 0.15/0.38 (step @p365 :rule cong :premises (@p364) :args (@t36)) % 0.15/0.38 (step @p366 :rule trans :premises (@p5 @p365)) % 0.15/0.38 (step @p367 :rule ho_cong :premises (@p366 @p73)) % 0.15/0.38 (step @p368 :rule ho_cong :premises (@p367 @p258)) % 0.15/0.38 (step @p369 :rule cong :premises (@p277 @p368) :args (@t46)) % 0.15/0.38 (step @p370 :rule cong :premises (@p369) :args (@t47)) % 0.15/0.38 (step @p371 :rule ho_cong :premises (@p6 @p74)) % 0.15/0.38 (step @p372 :rule ho_cong :premises (@p371 @p73)) % 0.15/0.38 (step @p373 :rule ho_cong :premises (@p372 @p282)) % 0.15/0.38 (step @p374 :rule nary_cong :premises (@p373 @p370) :args (@t48)) % 0.15/0.38 (step @p375 :rule trans :premises (@p374 @p289)) % 0.15/0.38 (step @p376 :rule cong :premises (@p375) :args (@t50)) % 0.15/0.38 (step @p377 :rule trans :premises (@p7 @p376)) % 0.15/0.38 (step @p378 :rule ho_cong :premises (@p377 @p74)) % 0.15/0.38 (step @p379 :rule ho_cong :premises (@p378 @p73)) % 0.15/0.38 (step @p380 :rule ho_cong :premises (@p379 @p216)) % 0.15/0.38 (step @p381 :rule refl :args (@t15)) % 0.15/0.38 (step @p382 :rule cong :premises (@p381 @p380) :args (@t21)) % 0.15/0.38 (step @p383 :rule cong :premises (@p382) :args (@t22)) % 0.15/0.38 (step @p384 :rule cong :premises (@p206 @p383) :args (@t23)) % 0.15/0.38 (step @p385 :rule cong :premises (@p384) :args (@t24)) % 0.15/0.38 (step @p386 :rule trans :premises (@p385 @p208)) % 0.15/0.38 (step @p387 :rule eq_resolve :premises (@p2 @p386)) % 0.15/0.38 (step @p388 :rule not_implies_elim2 :premises (@p387)) % 0.15/0.38 (step @p389 :rule not_implies_elim1 :premises (@p387)) % 0.15/0.38 (step @p390 :rule cnf_equiv_pos1 :args ((= tptp.lamProp @t76))) % 0.15/0.38 (step @p391 :rule chain_resolution :premises (@p390 @p389 @p388) :args ((@list false true) (@list tptp.lamProp @t76))) % 0.15/0.38 (step @p392 :rule ho_cong :premises (@p176 @p211)) % 0.15/0.38 (step @p393 :rule trans :premises (@p392 @p158)) % 0.15/0.38 (step @p394 :rule cong :premises (@p202 @p393) :args (@t228)) % 0.15/0.38 (step @p395 :rule cong :premises (@p394) :args (@t229)) % 0.15/0.38 (step @p396 :rule trans :premises (@p395 @p70)) % 0.15/0.38 (step @p397 :rule cong :premises (@p206 @p396) :args ((= tptp.lamProp @t229))) % 0.15/0.38 (step @p398 :rule refl :args (@t10)) % 0.15/0.38 (step @p399 :rule ho_cong :premises (@p379 @p398)) % 0.15/0.38 (step @p400 :rule cong :premises (@p381 @p399) :args (@t16)) % 0.15/0.38 (step @p401 :rule cong :premises (@p400) :args (@t18)) % 0.15/0.38 (step @p402 :rule cong :premises (@p206 @p401) :args (@t19)) % 0.15/0.38 (step @p403 :rule trans :premises (@p402 @p397)) % 0.15/0.38 (step @p404 :rule eq_resolve :premises (@p1 @p403)) % 0.15/0.38 (step @p405 false :rule contra :premises (@p404 @p391)) % 0.15/0.38 ) % 0.15/0.38 % SZS output end Proof % 0.15/0.38 % cvc5 exiting %------------------------------------------------------------------------------